The requirement to keep a system like this stable is a positive optical spring constant and a positive damping coefficient [1]}, [2]} which is not the case for our system. To keep the configuration of the cavity stable we employ a feedback loop actuating on an amplitude modulator (\(\mathrm {AM}_2\)  in Fig REF ). This ensures the cavity stays at a constant detuning during a measurement. This feedback loop uses a photodetector (\(\mathrm {PD_L}\)  in Fig REF ) in transmission of the cavity as the in-loop sensor and applies relevant correction signals to \(\mathrm {AM_2}\)  only for frequencies close to the optical spring frequency (i.e. above 100 kHz for the red curve in Fig REF ). This feedback loop does not provide any power stabilization of the injected beam. Another photodetector in transmission of the cavity is used to monitor the power noise of the transmitted beam, labeled \(\mathrm {PD_M}\) . Additional details describing the experimental setup can be found in [3]}, [4]}.
